Malcolm C. Smith
= Malcolm C. Smith
{c}
{tag=Physics author}
{wiki}
\b[Malcolm C. Smith] is a Cambridge researcher in <control theory> whose work connects <robust control> and <mechanical network synthesis> with physical system design. The Cambridge research profile identifies uncertainty, robustness and mechanical applications as themes of his work; the IEEE Control Systems Society independently identifies his Cambridge affiliation.<Malcolm Smith profile at the IEEE Control Systems Society>[IEEE affiliation entry; supplementary Cambridge research-profile entry, Research interests]{ref}
His 2002 paper <Synthesis of Mechanical Networks: The Inerter by Malcolm C. Smith> introduced the <inerter> as a two-terminal mechanical element. Its ideal terminal force is proportional to relative acceleration,
$$
F=b(\ddot x_1-\ddot x_2),
$$
where $b$ is <mechanical inertance>. Both terminals can move, so equal terminal accelerations produce zero force in this ideal constitutive relation. This makes the element useful for synthesizing mechanical responses through networks, alongside springs and dampers.<Synthesis of Mechanical Networks: The Inerter by Malcolm C. Smith>[Abstract and pp1648–1651, two-terminal element and physical realizations]{ref}
For an original ideal transmission example, relative terminal displacement drives a <flywheel> with angle $\theta=(x_1-x_2)/r$. With <moment of inertia> $J$, its kinetic energy is
$$
T=\tfrac12J\dot\theta^2=\tfrac12\frac{J}{r^2}(\dot x_1-\dot x_2)^2,
$$
so equivalent <mechanical inertance> is $b=J/r^2$. Choosing $J=0.002\,\mathrm{kg\,m^2}$ and $r=0.01\,\mathrm m$ gives $b=20\,\mathrm{kg}$. A relative acceleration $5\,\mathrm{m\,s^{-2}}$ then gives $100\,\mathrm N$. The coefficient has mass units, but it is not a statement that the flywheel's physical mass is20kilograms.
The calculation neglects friction, compliance and transmission inertia beyond the chosen flywheel. It illustrates the design idea, not measured performance of a particular device. The https://ieeecss.org/contact/malcolm-smith[IEEE Control Systems Society profile] includes a labeled headshot.